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Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design

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Progress in Cryptology – AFRICACRYPT 2011 (AFRICACRYPT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6737))

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Abstract

We introduce the Inhomogeneous Simultaneous Approximation Problem (ISAP), an old problem from the field of analytic number theory. Although the Simultaneous Approximation Problem (SAP) is already known in cryptography, it has mainly been considered in its homogeneous instantiation for attacking schemes. We take a look at the hardness and applicability of ISAP, i.e., the inhomogeneous variant, for designing schemes.

More precisely, we define a decisional problem related to ISAP, called DISAP, and show that it is NP-complete. With respect to its hardness, we review existing approaches for solving related problems and give suggestions for the efficient generation of hard instances. Regarding the applicability, we describe as a proof of concept a bit commitment scheme where the hiding property is directly reducible to DISAP. An implementation confirms its usability in principle (e.g., size of one commitment is 6273 bits and execution time is in the milliseconds).

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Author information

Authors and Affiliations

  1. Group for Theoretical Computer Science and Data Security, Universität Mannheim, Germany

    Frederik Armknecht

  2. FHDW Hannover, Germany

    Carsten Elsner

  3. Institute of Applied Mathematics, Leibniz Universität Hannover, Germany

    Martin Schmidt

Authors
  1. Frederik Armknecht
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  2. Carsten Elsner
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  3. Martin Schmidt
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université de Caen, Campus II, Boulevard Maréchal Juin, BP 5186, 14032, Caen Cedex, France

    Abderrahmane Nitaj

  2. École normale supérieure - CNRS - INRIA, Paris, France

    David Pointcheval

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Armknecht, F., Elsner, C., Schmidt, M. (2011). Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design. In: Nitaj, A., Pointcheval, D. (eds) Progress in Cryptology – AFRICACRYPT 2011. AFRICACRYPT 2011. Lecture Notes in Computer Science, vol 6737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21969-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-21969-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21968-9

  • Online ISBN: 978-3-642-21969-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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